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Sharp well-posedness for the Chen-Lee equation
Low regularity solutions for the (2+1)-dimensional Maxwell-Klein-Gordon equations in temporal gauge
1. | Fachbereich Mathematik und Naturwissenschaften, Bergische Universität Wuppertal, Gaußstr. 20, 42119 Wuppertal |
References:
[1] |
P. d'Ancona, D. Foschi and S. Selberg, Product estimates for wave-Sobolev spaces in 2+1 and 1+1 dimensions, Contemporary Math., 526 (2010), 125-150.
doi: 10.1090/conm/526/10379. |
[2] |
M. Beals, Self-spreading of singularities for solutions to semilinear wave equations, Annals Math., 118 (1983), 187-214.
doi: 10.2307/2006959. |
[3] |
M. Czubak and N. Pikula, Low regularity well-posedness for the 2D Maxwell-Klein-Gordon equation in the Coulomb gauge, Comm. Pure Appl. Anal., 13 (2014), 1669-1683.
doi: 10.3934/cpaa.2014.13.1669. |
[4] |
S. Klainerman and M. Machedon (Appendices by J. Bougain and D. Tataru), Remark on Strichartz-type inequalities, Int. Math. Res. Notices, 5 (1996), 201-220.
doi: 10.1155/S1073792896000153. |
[5] |
S. Klainerman and M. Machedon, On the Maxwell-Klein-Gordon equation with finite energy, Duke Math. J., 74 (1994), 19-44.
doi: 10.1215/S0012-7094-94-07402-4. |
[6] |
M. Machedon and J. Sterbenz, Almost optimal local well-posedness for the (3+1)-dimensional Maxwell-Klein-Gordon equations, J. AMS, 17 (2004), 297-359.
doi: 10.1090/S0894-0347-03-00445-4. |
[7] |
V. Moncrief, Global existence of Maxwell-Klein-Gordon fields in (2+1)-dimensional spacetime, J. Math. Phys., 21 (1980), 2291-2296.
doi: 10.1063/1.524669. |
[8] |
H. Pecher, Low regularity local well-posedness for the Maxwell-Klein-Gordon equations in Lorenz gauge, Adv. Diff. Equ., 19 (2014), 359-386. |
[9] |
H. Pecher, Unconditional global well-posedness in energy space for the Maxwell-Klein-Gordon system in temporal gauge, Adv. Diff. Equ., 20 (2015), 1009-1032. |
[10] |
S. Selberg, Multilinear Space-time Estimates and Applications to Local Exisatence Theory for Nonlinear Wave Equations, PhD. Thesis Princeton, 1999. |
[11] |
S. Selberg, Anisotropic bilinear $L^2$ estimates related to the 3D wave equation, Int. Math. Res. Not., 2008, art. ID rnn107. |
[12] |
S. Selberg and A. Tesfahun, Finite energy global well-posedness of the Maxwell-Klein-Gordon system in Lorenz gauge, Comm. PDE, 35 (2010), 1029-1057.
doi: 10.1080/03605301003717100. |
[13] |
T. Tao, Multilinear weighted convolutions of $L^2$-functions and applications to non-linear dispersive equations, Amer. J. Math., 123 (2001), 838-908. |
[14] |
T. Tao, Local well-posedness of the Yang-Mills equation in the temporal gauge below the energy norm, J. Diff. Equ., 189 (2003), 366-382.
doi: 10.1016/S0022-0396(02)00177-8. |
[15] |
J. Yuan, Global solutions of two coupled Maxwell systems in the temporal gauge, Discr. Cont. Dyn. Syst., 36 (2016), 1709-1719.
doi: 10.3934/dcds.2016.36.1709. |
show all references
References:
[1] |
P. d'Ancona, D. Foschi and S. Selberg, Product estimates for wave-Sobolev spaces in 2+1 and 1+1 dimensions, Contemporary Math., 526 (2010), 125-150.
doi: 10.1090/conm/526/10379. |
[2] |
M. Beals, Self-spreading of singularities for solutions to semilinear wave equations, Annals Math., 118 (1983), 187-214.
doi: 10.2307/2006959. |
[3] |
M. Czubak and N. Pikula, Low regularity well-posedness for the 2D Maxwell-Klein-Gordon equation in the Coulomb gauge, Comm. Pure Appl. Anal., 13 (2014), 1669-1683.
doi: 10.3934/cpaa.2014.13.1669. |
[4] |
S. Klainerman and M. Machedon (Appendices by J. Bougain and D. Tataru), Remark on Strichartz-type inequalities, Int. Math. Res. Notices, 5 (1996), 201-220.
doi: 10.1155/S1073792896000153. |
[5] |
S. Klainerman and M. Machedon, On the Maxwell-Klein-Gordon equation with finite energy, Duke Math. J., 74 (1994), 19-44.
doi: 10.1215/S0012-7094-94-07402-4. |
[6] |
M. Machedon and J. Sterbenz, Almost optimal local well-posedness for the (3+1)-dimensional Maxwell-Klein-Gordon equations, J. AMS, 17 (2004), 297-359.
doi: 10.1090/S0894-0347-03-00445-4. |
[7] |
V. Moncrief, Global existence of Maxwell-Klein-Gordon fields in (2+1)-dimensional spacetime, J. Math. Phys., 21 (1980), 2291-2296.
doi: 10.1063/1.524669. |
[8] |
H. Pecher, Low regularity local well-posedness for the Maxwell-Klein-Gordon equations in Lorenz gauge, Adv. Diff. Equ., 19 (2014), 359-386. |
[9] |
H. Pecher, Unconditional global well-posedness in energy space for the Maxwell-Klein-Gordon system in temporal gauge, Adv. Diff. Equ., 20 (2015), 1009-1032. |
[10] |
S. Selberg, Multilinear Space-time Estimates and Applications to Local Exisatence Theory for Nonlinear Wave Equations, PhD. Thesis Princeton, 1999. |
[11] |
S. Selberg, Anisotropic bilinear $L^2$ estimates related to the 3D wave equation, Int. Math. Res. Not., 2008, art. ID rnn107. |
[12] |
S. Selberg and A. Tesfahun, Finite energy global well-posedness of the Maxwell-Klein-Gordon system in Lorenz gauge, Comm. PDE, 35 (2010), 1029-1057.
doi: 10.1080/03605301003717100. |
[13] |
T. Tao, Multilinear weighted convolutions of $L^2$-functions and applications to non-linear dispersive equations, Amer. J. Math., 123 (2001), 838-908. |
[14] |
T. Tao, Local well-posedness of the Yang-Mills equation in the temporal gauge below the energy norm, J. Diff. Equ., 189 (2003), 366-382.
doi: 10.1016/S0022-0396(02)00177-8. |
[15] |
J. Yuan, Global solutions of two coupled Maxwell systems in the temporal gauge, Discr. Cont. Dyn. Syst., 36 (2016), 1709-1719.
doi: 10.3934/dcds.2016.36.1709. |
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